No, turn it off.

What computers do when they're on and not doing anything:  
- waste electrical energy (which is not that negligible) <-- nowadays, wars are fought over energy, remember ?  
- produce heat (which is not that negligible)  
(neither of these are making our planet a nicer place to live)  
- cost you money  

What computers do when they're off:  
- don't cost anything  
- helps to ease up that air condition unit  
- most of their parts are not made up for 24h work load  

Hard discs do not suffer that much from turning off/on, as has been presented here. I've got three of them in the drawer/attic, which range from 15-10 years old, and have been turned off/on, regularly for 10 years, several times a day. All still work (I'm not using them of course, but they still work).

The price of energy has been calculated by someone already.